We introduce the notion of an adequate moduli space. The theory of adequate moduli spaces provides a framework for studying algebraic spaces which geometrically approximate algebraic stacks with reductive stabilizers in characteristic p. The definition of an adequate moduli space generalizes the existing notion of a good moduli space to characteristic p (and mixed characteristic). The most impo...

THE HILBERT SPACE OF PROBABILITY MASS FUNCTIONS AND APPLICATIONS ON PROBABILISTIC INFERENCE Bayramog̃lu, Muhammet Fatih Ph.D., Department of Electrical and Electronics Engineering Supervisor : Assoc. Prof. Dr. Ali Özgür Yılmaz September 2011, 123 pages The Hilbert space of probability mass functions (pmf) is introduced in this thesis. A factorization method for multivariate pmfs is proposed by u...

Then Γ acts cocompactly on X and X , and the orbit spaces X/Γ and X /Γ are closed manifolds with contractible universal covers. The only nontrivial homotopy groups are thus the fundamental groups, π1(X/Γ) ∼= Γ ∼= π1(X /Γ). It follows that there is a homotopy equivalence X/Γ X /Γ which can be lifted to a map f : X X . This map f can then be shown to be a quasi-isometry. Recall that a (not necess...

This article establishes the algebraic covering theory of quandles. For every connected quandle Q with base point q ∈ Q, we explicitly construct a universal covering p : (Q̃, q̃) → (Q,q). This in turn leads us to define the algebraic fundamental group π1(Q,q) := Aut(p) = {g ∈ Adj(Q)′ | qg = q}, where Adj(Q) is the adjoint group of Q. We then establish the Galois correspondence between connected c...

In this paper we study when a bipartite graph is a covering of a non-bipartite graph. We give a characterization of all coverings in terms of factoring the covering map through the canonical double covering. We also consider regular bipartite coverings described in terms of voltage assignments. We give an algebraic characterization of such coverings involving the subgroup generated by voltages ...

We therefore consider only connected groups, which we often choose to regard as connected reductive algebraic groups over R. This paper classifies connected, simply connected, acceptable, compact groups. As a byproduct of the method, we also treat the non-simply connected, exceptional groups. It turns out that the only acceptable, exceptional group is G2. The original motivation for this questi...

Let D ≥ 1 be an integer. The set of unitary highest weight modules of Spin(2, D + 1) is known to be nonempty. Inside this set, there is a special subset consisting of those modules that can be realized by the Hilbert space of bound states for a generalized hydrogen atom in dimension D. Here an algebraic characterization of this special subset is given.

Several interesting numbers such as the homotopy invariant Lefschets number L(f), Nielsen N(f), fixed point index i(X, f,U) and Reidemeister R(f) play important roles in study of theorems. The gives more geometric information about points than other numbers. However is hard to compute general. To number, Jiang related it R(f ) induced homomorphism f : 1(X) when X a lens space or an H-space (Jia...

Let $X$ be a reflexive Banach space, $T:Xto X$ be a nonexpansive mapping with $C=Fix(T)neqemptyset$ and $F:Xto X$ be $delta$-strongly accretive and $lambda$- strictly pseudocotractive with $delta+lambda>1$. In this paper, we present modified hybrid steepest-descent methods, involving sequential errors and functional errors with functions admitting a center, which generate convergent sequences ...

Cumulants represent a natural language for expressing macroscopic properties of a solid. We show that cumulants are subject to a nontrivial geometry. This geometry provides an intuitive understanding of a number of cumulant relations which had been obtained so far by using algebraic considerations. We give general expressions for their infinitesimal and finite transformations and represent a cu...